The existence and the structure of uniform global attractors for nonautonomous reaction-diffusion systems without uniqueness (Q1017553)

The authors prove existence of attractor for weak solutions to the following reaction-diffusion system \(\partial_t u - a \Delta u + f(u,t) = g(x,t)\) (with the Dirichlet boundary condition) with a nonlinearity \(f(u,t)\) satisfying suitable coercivity and growth condition on \(u\), and an external force \(g(x,t)\) satisfying suitable growth restriction for \(t\to\infty\).